Graph this system of equations and solve. $-5x+3y = -3$ $18x-6y = 30$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $-5x+3y = -3$ , to slope-intercept form. $y = \dfrac{5}{3} x - 1$ The y-intercept for the first equation is $-1$ , so the first line must pass through the point $(0, -1)$ The slope for the first equation is $\dfrac{5}{3}$ . Remember that the slope tells you rise over run. So in this case for every $5$ positions you move up You must also move $3$ positions to the right. $3$ positions to the right. $5$ positions up from $(0, -1)$ is $(3, 4)$ Graph the blue line so it passes through $(0, -1)$ and $(3, 4)$ Convert the second equation, $18x-6y = 30$ , to slope-intercept form. $y = 3 x - 5$ The y-intercept for the second equation is $-5$ , so the second line must pass through the point $(0, -5)$ The slope for the second equation is $3$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up You must also move $1$ positions to the right. $1$ position to the right. $3$ positions up from $(0, -5)$ is $(1, -2)$ Graph the green line so it passes through $(0, -5)$ and $(1, -2)$ The solution is the point where the two lines intersect. The lines intersect at $(3, 4)$.